Question

An object 1.25 cm tall is placed on the x-axis at x = -100 cm. A biconvex lens with a focal length of +50 cm is placed at the origin. A biconcave lens with a focal length of -20 cm is placed on the x-axis at x = 90 cm.

a) Where is the location of the image formed by the convex lens?

b) Where is the location of the final image formed by the concave lens?

Answer 1

a)
Object distance, u1 = 100 cm
Focal length, f1 = 50 cm
Consider v1 as the image distance.
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Using the formula, 1 / f1 = 1 / u1 + 1 / v1,
1 / v1 = 1 / f1 - 1 / u1
= (u1 - f1) / (f1 * u1)
v1 = (f1 * u1) / (u1 - f1)
= (50 * 100) / (100 - 50)
= 100 cm, the image is at the right side of the lens
The image is at 0 + 100 = 100 cm on the x-axis

b)
Object distance, u2 = 100 - 90 = 10 cm, the object is at the right side of the lens
Focal length, f2 = - 20 cm
Using the formula, 1 / f2 = 1 / u2 + 1 / v2,
1 / v2 = 1 / f2 - 1 / u2
= (u2 - f2) / (f2 * u2)
v2 = (f2 * u2) / (u2 - f2)
= (-20 * 100) / (10 - (-20))
= - 6.67 cm, which is at the right side of the lens
The image is at 90 + 6.67 = 96.67 cm on the x-axis